{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating hydrogen bonds: the basics\n",
    "\n",
    "We will find the hydrogen bonds in a box of water in order to demonstrate the basic usage of HydrogenBondAnaysis.\n",
    "\n",
    "**Last updated:** December 2022\n",
    "\n",
    "**Minimum version of MDAnalysis:** 2.0.0-dev0\n",
    "\n",
    "**Packages required:**\n",
    "    \n",
    "* MDAnalysis (<a data-cite=\"michaud-agrawal_mdanalysis_2011\" href=\"https://doi.org/10.1002/jcc.21787\">Michaud-Agrawal *et al.*, 2011</a>, <a data-cite=\"gowers_mdanalysis_2016\" href=\"https://doi.org/10.25080/Majora-629e541a-00e\">Gowers *et al.*, 2016</a>)\n",
    "* MDAnalysisTests\n",
    "* [numpy](https://numpy.org)\n",
    "* [matplotlib](https://matplotlib.org)\n",
    "\n",
    "**See also**\n",
    "\n",
    "* [Calculating hydrogen bonds: advanced selections](hbonds-selections.ipynb)\n",
    "* [Calculating hydrogen bond lifetimes](hbonds-lifetimes.ipynb)\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "    \n",
    "**Note**\n",
    "\n",
    "Please cite [Smith et al. (2018)](http://dx.doi.org/10.1039/C9CP01532A) when using HydrogenBondAnaysis in published work.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "import numpy as np\n",
    "np.set_printoptions(linewidth=100)\n",
    "import pandas as pd\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import MDAnalysis as mda\n",
    "from MDAnalysis.tests.datafiles import waterPSF, waterDCD\n",
    "from MDAnalysis.analysis.hydrogenbonds import HydrogenBondAnalysis\n",
    "\n",
    "# the next line is necessary to display plots in Jupyter\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading files"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will load a small water-only system containing 5 water molecules and 10 frames then find the hydrogen bonds present at each frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lily/pydev/mdanalysis/package/MDAnalysis/coordinates/DCD.py:165: DeprecationWarning: DCDReader currently makes independent timesteps by copying self.ts while other readers update self.ts inplace. This behavior will be changed in 3.0 to be the same as other readers. Read more at https://github.com/MDAnalysis/mdanalysis/issues/3889 to learn if this change in behavior might affect you.\n",
      "  warnings.warn(\"DCDReader currently makes independent timesteps\"\n"
     ]
    }
   ],
   "source": [
    "u = mda.Universe(waterPSF, waterDCD)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "    \n",
    "**Warning**\n",
    "\n",
    "It is **highly recommended** that a topology with bond information is used (e.g. PSF, TPR, PRMTOP), as this is the only way to guarantee the correct identification of donor-hydrogen pairs.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hydrogen bonds\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In molecular dynamics simulations, hydrogen bonds are typically identified via the following geometric criteria:\n",
    "\n",
    "1. the donor-acceptor distance ($r_{DA}$) must be less than a specified cutoff, typically 3 Å\n",
    "2. the donor-hydrogen-acceptor angle ($\\theta_{DHA}$) must be greater than a specified cutoff, typically 150°"
   ]
  },
  {
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NwOkG2OzeKFHZN92uqufUj6qe7jiZlqZ+ihscUOPS7+OXZWZ1OwOqaTu7Ale/BLGiH9l5498tziwm/n4BAAAAoOjx6/+5sLCwsLDQez/FHRaaRUREREREWK/g5EyLjOl6TLU+0V0v2V0P6fZD179du6bjYPf43B5fU/t2tzdt2rRp06ZEvXr16tWr1+/7a5c7d+7cuXOHaP78+fPnz1c/0Ks7LnbHSVbKBKem7XRLt+3JBK4sZK1atWrVqlWJwsLCwsLC/HvwAYBghL8vK1euXLlypf8PKLOw9tNPP/3000/981vcSEtLS0tLc89eYmJiYmKie/ZKCqbCVp4Pt2vXrl27dt71y20GDBgwYMAAKxO+KZzR9t///ve///1v9/vnFdu2bdu2bRvR2rVr165dq9+O54XiOofhB/10gbAVAAAAAKBkA2ErAAB4BGdC4cw8LBDzGjHw47SdKqDkVj91A1em7U37I7ZXBaZKGnzcMmGr6Xn0Cg5MyDISuZ1h1a3jkgl2vR4/tsv+ypYtW7ZsWSuDCX8GAAAAQODA6wyvuXLlypUrV7z3U9zheRYLkjmTJgvRRFTzadW6RdZO155pe91+20W3fbCt05wel+l2FmY0bNiwYcOG5v2VwYIDu0It2bqbEbebCkpN2+sKVO36UfnVLVmgx5nPZAISAMDv6datW7du3ewL1ZwyYsSIESNGEJ07d+7cuXP++w923BK28rysbdu2bdu2dW6vpGEqbGVBa7D+X82cOXPmzJlE1apVq1atmnn7jz766KOPPnK/X27Db+wYM2bMmDFj9Oer3bt37969O1GPHj169Oghr4eMrQAAAAAAwAQIWwEAwCM40MAZjm7dunXr1i3nGUdk6Aa0dG9E6KI6nkBBdzxl+03PU6COgwrTgJzXxyfa9zqThm5GUxl2z7vML4+zqX9TZAJatwXAAAAAAHAPFjR5DYSt7sDzqT/84Q9/+MMfrFd0csnbZfNw0/WGbD1jKiDUtavbL5V/U7u623VLu+1NhZVel7Lj4Ots7NixY8eOdV9Ysm7dunXr1hEdPnz48OHD7gujTY/XruBV/OyWEFXXv6zkTKyVKlWqVKmSJQxp0KBBgwYNrEx4AAB95syZM2fOHKLmzZs3b97cP7+5ubm5ublEQ4YMGTJkiPn9n5KOqaBSBgta8UC3GRzn2Ldv3759+/TbJSUlJSUledcvr+EHC1nwaQpnbBXnL4HGkiVLlixZQnTw4MGDBw+q6/ObvzhTq4o6derUqVNHvz+XLl26dOkS3iQCAAAAAFBSgbAVAAA8hm9MqjJb2g3U6N4IUQWMdO0H2o0Xu+Mna2+6XRWgsttPr9Dth6xUBeZk/pziVFhpKtA0Fbja7Z+qnel1JWuvW5/PK/eLA6cQtgIAAACBR5UqVapUqeL9K6ezs7Ozs7O9s1/S4DcKcGb8mJiYmJgYooiIiIiICCswbHceaHcdYreU+dX173Y9u+3t2jc9XreP367fmjVr1qxZk2jw4MGDBw/+/XHYhe0vXrx48eLFRDdu3Lhx44Z7x6ny61YpW+/aFbrq2pXZ4ftJ/PvAvx98HqtXr169enVrPwBAHxaE86u2/RaIb9q0adOmTUQLFy5cuHChf36DlatXr169epXo+PHjx48fd24vMTExMTHRuZ2Sxu7du3fv3k109+7du3fv6rcrLuPNgnTT+6Xnz58/f/480ZkzZ86cOeNd/+zC677p06dPnz5dv924cePGjRtH1KhRo0aNGqnr16tXr169evr2eX6UlZWVlZWl3w4AAAAAABQPIGwFAACP4Bsb4ismZYELp+gGiFT1Zcdh6k/Xvleo/KnGRfys2q4KVPl9/LronjddQavu8Qb6uIjIvgdeCz5Nx1PWzjRzEAtkKlSoUKFCBevVbAAAAAAIHFggyQJXr0DGVm/gzJksaG3SpEmTJk2s86m7ntCdz+vOu92az8vmp6r2pv10ur2o8ft4xe38Ku74+Pj4+Hj9fqu4du3atWvXiN5777333nvPf+Gu0/ayceNSJVjVFbyyYFV3vcb3lxo2bNiwYUOiypUrV65c2b3zBkBJplmzZs2aNSN67bXXXnvtNf/9T548efLkyUQHDhw4cOCA//6DhbS0tLS0NPf+14uL0NJvTDPm8v3T4jLe0dHR0dHRRC1atGjRooV5+6NHjx49etT9fjnl5Zdffvnll4ny8vLy8vLU9aOioqKiooimTp06depUfT+ccd6UU6dOnTp1yrwdAAAAAAAIbiBsBQAAj+AbNiwIU2VSshvgUdlTtTf97BRd+7qBKLt+ZXZN/atKU0GhShjrtB+6+2UBt3v37t27d8/9V6Spzqfp+db1p7Krm1HVrn/VuDs974xoV5aRlvezUIYzlXidCQ4AAAAA9qlatWrVqlW9s4+Mre4ivkmAhWoc4OUHi0zne6rP4nbZfFFmR3f+rNsPVX9U/bB7nLrb/Sp1/ds9Lt3zMGrUqFGjRlmvuHeLnTt37ty5k2j79u3bt2+X1/P7fOle73bX0brtxXqy9WD58uXLly9vZWblV/jy7wUAwD0mTJgwYcIEoocffvjhhx/2z++dO3fu3LlD1K9fv379+lmvegf/CQtb3aJ9+/bt27d3z15JwfQ8iA9wFRfatWvXrl0783YnT548efKk+/2xC8/XVq5cuXLlSv12s2bNmjVrFlF4eHh4eLh+O36wz3TeCWErAAAAAEDJBMJWAADwCA5UciYeLk1fca4KTMkCMbr2Tfuha8/Ujt3jUfXL7fq6/dcVtJpuN/Wjsqtb//79+/fv37dK1XjIxtMppvZ0++nUn93rRHVeVOMq7tcNnIqIflnYWrZs2bJly1q/XwAAAAAIPKpVq1atWjXv7POrxG/evHnz5k3v/JRU+EEifrU4B3hDQkJCQkKseuK80e78U8R03mo6z7TrT3e7aX9V/dE9Dqfj5Fa/dNurtrNAcsyYMWPGjHH/zRQrVqxYsWLF74Xybp93EbvnQdyuuz4X66s+q0qGhUC1atWqVauWlSmOBa8AAPfg+yGrVq1atWqV/0K8jIyMjIwMK3Mi+E/cErbyq9Br1qxZs2ZN5/ZKCvz/ZHoeOnTo0KFDB+/6VVQ0aNCgQYMG5u2uX79+/fp19/tjCp/P0aNHjx49Wn8ezJl3BwwYMGDAAPv+TTO3QtgKAAAAAFAygbAVAAA8hjO2lilTpkyZMtYNUsY0sCKiCuTYxTRAZGrH7nbZZ7+2q45Pdzx0A1m6AlSxdLu9W+dPNV6m42i3vcqe6XiJdmTn263j1fUrsyvbL2aa5gxiyNgKAAAABC5eC1uZQMssVFzhTIz8SuSwsLCwsDD3BZ6682m7pSjMszvvle2XfVahW9/Urlt41T/d8WzZsmXLli2JunXr1q1bN337KgoLCwsLC4nefvvtt99+23ojiKw/sutJdX3orrt0/aja2+23rJ5M2MoCrNjY2NjYWDx4CIAfsODxvffee++99/z3v2jRokWLFhF99dVXX331lf/+Aw1+g9TevXv37t3r3B4L84AZmZmZmZmZRLm5ubm5ufrtiquwlTOPmsIPDhY177///vvvv6//veK4Fv8+OX0QCsJWAAAAAACgA4StAADgEWLGVha2ckYNFo7pBkjEz3YDWar2poEau/adbtdtpzt+dsffdDzslnYFr6bbxZIDjrIAn+m4uj1epteBrl8Vbh2P7vip+qFbXwX/TnGmVghbAQAAgMAnJiYmJibGez9Hjhw5cuSI935KOpwZjgWunMGV52l2582mpQzT+bRdv7r7i6ofXpW6fnWPW3b+ZHaYgQMHDhw4kKh27dq1a9eW2zPl2LFjx44dI1q/fv369evN1y92x0XVXleAquvftN9iyd/7uLi4uLg4S/gRGRkZGRn5+wemAQDe0bt37969exMNHjx48ODB/vnl34MhQ4YMGTKE6PLly5cvX/bPf6DBwjt+UMIpCQkJCQkJzu2UNFJTU1NTU83bFVdhK795wRSe1xcV165du3btGtGUKVOmTJmi327o0KFDhw4latOmTZs2bZz3w1TYmpWVlZWV5dwvAAAAAAAILnALDAAAfIJfJcmBStmrJVWBEdV2p4EhU3T7qxtosovdcXMbp37sBtDEUhaYM83UKssYozpu3XHQvQ7cvo506+s+eW7aD6fXq+l4q8aNj5MzgoWHh4eHh0PYCgAAAAQDLHzymqNHjx49etR7P+5EQGcAACAASURBVCUdnn+xgI0z8vIDkrJ5ve4bBhhVPd39qvpuvbnALnbn2yUVHhee/48dO3bs2LHWg7lu8eWXX3755ZdWJmhVRla76yfZdan7vZGtg8X9qgdBZf2RfY85U2SXLl26dOliCT94veY0QxoAwJzFixcvXryYqGHDhg0bNvTPb3Z2dnZ2NtEzzzzzzDPPlNz/r7S0tLS0NPfsIWOrPXbs2LFjxw79+tWrV69evTpRgwYNGjRo4F2/ioqCgoKCggLzdpUrV65cubL7/dGFBa0scFXBmWmTk5OTk5Pd64fdjK0l9XcQAAAAAKCkAmErAAD4BAeGRKGYboDGbmBHtxTbmdqx21+77e2Om9Nx0i3dyvgis+s0Y6tqv0zQqhp/2WfVeVCdH7u47d9pf1R+vLIv88PnlzPziv45YIrAKQAAABC4NG7cuHHjxt77gbDVH3jexRmg+BXkVatWrVq1KtH9+/fv379v/5Xrpm9icFrK7Or6U9VTCSJN/dsdBxlOx83uccjGR9cOU6tWrVq1ahE9+eSTTz75pLxfpvD6Y8mSJUuWLCG6ffv27du33eu/3XGW+VWtq1X1VOt3zsDKD0Lz952FJJzZDeszAIoOvp+bkpKSkpLivuBfxTfffPPNN99Yrw4vabglbOXz2Lx58+bNmzu3V9IwzdjasWPHjh07etefoiY/Pz8/P9+8HWdm95uff/75559/Jlq2bNmyZcv0282YMWPGjBnW/MQtTIWtt27dunXrFtGlS5cuXbrkXj8AAAAAAEBgA2ErAAD4xB/+8Ic//OEP1iu++bNp4EUVgFHVV7U3tee0vq5/1Xa7+3X9BHqpErjK6qvsqMZHhmy/qp1TZP2V7dftp2m/VfZVdlXnW9VPU/9ixlb+nQIAAABA4NOoUaNGjRp57wfCVn9hwQxnuoqOjo6OjrYyubLQzXQ+W1SlrB+6/dNt7/fxqvzp4tY4Oh0PWfvHH3/88ccfJ2rWrFmzZs30j0sFZyJcu3bt2rVr3TsOsdRdJ7tdqgStXPL3vU6dOnXq1CGKiYmJiYmxMjXjDRoABA7x8fHx8fFEr7zyyiuvvOK///Hjx48fP77kzcvcEra2b9++ffv2+F01hYWEnDFTl+KeGTcvLy8vL8+8nd/CVp6XPP/8888//7z1gJEKFoCPGDFixIgR7veLH+AzxfQ6BAAAAAAAwQ2ErQAA4BOcgSMkJCQkJMT6LGbEZFSBJVkAym57WSlDt76uPbvHqWvPbntZv7xqp3s+dLeblroBP6fj4hSvx0XXr9N2qn6r7Mk+6/aD4Rv6/MpLfuUtAAAAAAIfzpzDmf68ggUURTX/K2nwepEfOOKMRg8++OCDDz5oBcR1H3ATEef/pvNlu/NuWT1xu6y/unZVqPzo4vT74LY/0/2q8WT4QbiRI0eOHDnSEly6xdatW7du3Uq0e/fu3bt3u7fOtdteNm5266n6xd/zdu3atWvXzsrEzQJ2/j0AAAQOU6dOnTp1KlFCQkJCQoJ/fgsLCwsLC4n69evXr18/ort37969e9c//37DAraLFy9evHjRub3iLrT0ih07duzYscO8XVJSUlJSkvv9CRSOHTt27Ngx83ZNmjRp0qSJ+/2RsWLFihUrVhDt3Llz586d+u0WLly4cOFC74TgELYCAAAAAAAdcEsMAAB8ggMRfCOAM7bydg5omGbeFPEqYGO3vWy/qr5pPafHpWvPdDzsjqtXpW7gWoVqXEzPr2q7aX9M7emOn1M7pv027ZdpfxlROMGvvgUAAABA8BAXFxcXF+ed/YKCgoKCAqLjx48fP37cOz/gv2EhIc/TWEgYFRUVFRVllRUrVqxYsaL5GxtETOefpvNSVT1Tga3Tfrt93H71w63jlp1/FZUrV65cuTLRc88999xzz6nrm7J69erVq1cT5ebm5ubm+rf+VbWXjZds3HTtcgbm+vXr169f3xpfXpfx959/DwAAgQPf301JSUlJSSGqUKFChQoV/PPPrxT/xz/+8Y9//MM/v37jVqZWBsJWe6SmpqampurX5zdCtWrVqlWrVt71q6j55ZdffvnlF/36PG+PjY2NjY31rl9Mfn5+fn6+JcTX5amnnnrqqaeIunTp0qVLF+/6Fx4eHh4ebs1/dIGwFQAAAACgZAFhKwAA+AQHIvjGJ2fe4JL3mwak7O732r6uf1k9cbvTenb9Ox1H3dKtQK5su2mg2y3/snE07b+snsqf7vlV1TcdF5kdmaDA7niZHpcIB0r51ZecUZo/AwAAACB44Ax/XuO2wADowetGFs5ER0dHR0dbmfbFN4LI5ot+vYqd8bqd1/X9KkXsHofd7ab++VXcnTp16tSpk/r61eXGjRs3btwgWr58+fLly9UZiO2Os6qe6RtMdEvxvhC/MYN/v1kIBAAIHjjjIGc29JtZs2bNmjWLaPPmzZs3b/bfv9e4Ne/k31/OfA/MMD0PPM7F9f7izZs3b968aS6wbN26devWrf17YGXatGnTpk3Tz3jM85DZs2fPnj3b+/4xpplbIWwFAAAAAChZQNgKAAA+wTcsOFMrP6HLT6SKmVtlgSZVoEWsp0Llx+l+lV9VYEhmz+lxq+qb2rGL235Mz7uq9Btd/6bXj2l71Wdd/05LWT9UN0DF/TL7okCCX2mLgCoAAAAQfDRr1qxZs2be+0lPT09PT/feD/jf4fUkC1tjYmJiYmKs+Rvv/+2333777Tf9N4EUdcnYrSeia0eGbj1d7I6H2/5V203Hf9CgQYMGDSKqUaNGjRo13OtvRkZGRkYG0Y8//vjjjz/a77e4X/Y9MP1+iPVlb94RSxb4VK9evXr16lbGNi7x5gwAgpfBgwcPHjzYynToF/z7MnDgwIEDB1oZr4sLbglbmzZt2rRpU6KIiIiIiAjn9koKhYWFhYWFRPv27du3b59+uw4dOnTo0MG7fhU1W7Zs2bJlizyzu4x27dq1a9fOs279/xw8ePDgwYNES5YsWbJkiX67yZMnT5482Vpf+EXdunXr1q2rXx/CVgAAAACAkgWErQAA4BMsNOOSXy1Xrly5cuXK/T5jK6MboFF91rWj60dENwCk8qu73Wl703FyOo6qdnbH0+m4mNo13W7a3m49u+1Nx0m23+1Xp6r6qRpnsV+ywCsLIPgVmPx7VFwzKgAAAADFmfbt27dv3957PxC2Fi28bixfvnz58uUtQWGjRo0aNWpkPUCpErQWtdDV6fxZ/Gza3q1S165X/nX9yfyrtouI9fhBuZEjR44cOdISVrvF559//vnnnxOdO3fu3Llz7l9nMgGqrh1d4Th/L2vXrl27dm2iFi1atGjRgqhOnTp16tSxHjTkTK4AgODl3Xfffffdd63vu1/8+uuvv/76K9GwYcOGDRvmn1+v4FeoHz58+PDhw87tJSYmJiYmOrdT0ti9e/fu3buJ7t27d+/ePf12SUlJSUlJ3vWrqPn666+//vpr83a9evXq1auX+/0RGTt27NixY4nu379///59df369evXr1+faOLEiRMnTvS+fyKmwtasrKysrCzPugMAAAAAAAIM3CoDAIAiggNAXIrCVt0AlVjKMjXqfpa1V9lVtRf3i3ZV9UzbyzA9Dl27snFyC9N+yOqrzr/derrXme51rNte1T+VH107qn6KT+jb7Y+qf6bjocrUxYIIfoUt/x4BAAAAIPho27Zt27ZtrYx/t2/fvn37tvt+fvnll19++cXKCIbMV/4ivsqc53F8Hm7dunXr1i2i7Ozs7Oxs+fqE3xjC80Oux9tV/lXzUPHBThXcjv2b+hE/6/qT1TddD8rsi/ZU9Zz6MbUrW1fIPstKFiT06NGjR48eROvWrVu3bp3942JYkLF8+fLly5cTvfzyyy+//LJ1/TsVnKpK2QOCqvpivaioqKioKCtjIL+KOCQkJCQkxPk4AQACB34Tzpo1a9asWUPUtWvXrl27WvdnvIYfCEhJSUlJSSHq379///79vffrNvw7+tFHH3300UfO7fEDBcCM1NTU1NRU/fo8j/PrgTu/4f91U2FrrVq1atWqRZSQkJCQkOBd//h7zxlldZk3b968efOKLnO8qbD1woULFy5csNY9nEAGAAAAAAAUTyBsBQCAIoIDGJwxkT/zjU7dQJJqvyqwJ9aTtRMDNbqBOdGurL1XAlfdgKSuIFeF7rgHK6px1K0vu45N7Zp+T3Tr2W2nm/FH176svQhfb7r1GVHYisAqAAAAELzw/zgLprzKrMrzDc7g1K1bt27durnvB+jBAgLOuM+ZW1n4d+zYsWPHjlmBX3F+KApZ+fzKBK6q9aAuqvWcal1lus6Tre9kfmT1RXTXM3bXPaZ2dNc1uvV11xUMC1s5w96JEydOnDihbqeCBQwsmO3Tp0+fPn1+30+/BK2ydZ9Y8nXDgo3Y2NjY2FhkZgWgJNCpU6dOnToRjR8/fvz48URz5syZM2eOf/6ff/75559/3nolvKlwrKhhgXDfvn379u1b1L0puZgKW5s3b968eXMrU3lx44cffvjhhx+ITp8+ffr0af12Tz755JNPPql+gMwuBQUFBQUFRJMmTZo0aZJ+u0ceeeSRRx4h6tmzZ8+ePd3vly6mv088H+Pz0KRJkyZNmnjVOwAAAAAAUNR4MIUGAACgAwcyOADNT8TydlkASRVoUgWe/LKr8mNaT7e9U/9OS6/82D0vqvMr++zUn8q/7n5TP7L2qn67Nd4qO7r1Ve10j1fczq8GLVeuXLly5awbzVwiwAoAAAAEP15nAmK2bdu2bds27/2A/xsWzvE8jzNDxsXFxcXFEVWvXr169epWJiPTB7HsZqhEGRwlI/tsWvJ1yK/CdjuD1ubNmzdv3mwJZ3Uzquo+cChrp1uyYKVChQoVKlQgqlOnTp06dYhiYmJiYmKIqlatWrVqVWucAADFn+Tk5OTkZKJWrVq1atXKP7/Xr1+/fv060YABAwYMGOBfxlhQPOD/tZ07d+7cuVO/HQupiyvvvPPOO++8Y97O68zJM2bMmDFjhvUgkC6bNm3atGnT79+04HfJD0aZcurUqVOnTpm3AwAAAAAAwQWErQAAUMRwQIMzt3KmHa8CgyKy7eJ+VcDHaXtTP6b17PbTFN1x9wrd41R91u236fHpXo9uXy+mmPo3HS+7x2/aPxEW0nNgNTIyMjIy0vrdKa6ZhgEAAICSRGJiYmJiovd+Nm7cuHHjRu/9ADPKlClTpkwZosqVK1euXNnKYMSCV5kQ1VTg6nZGTFO7Yj1Gd74us+fUrlfojqtYX9euzI9uP8T9LODs169fv3797B+3zP+HH3744YcfEuXn5+fn58v7IbtuVdtNvye8juIHlhs2bNiwYUOiP//5z3/+85+t7x8AoOTB92HWrl27du1a6/6vX3DGzVmzZs2aNcs/vyC4ycjIyMjIIMrNzc3NzdVv59c6xG/OnDlz5swZovXr169fv16/Hb/Zok2bNm3atHG/X5mZmZmZmUQLFy5cuHCh+/YDHQhbAQAAAABKBhC2AgBAEcMZEsPDw8PDw61AiCpwogok6e4XUe0X6+m217Urs29qV3dcTMfR1I5b9ryy69Z5062n23/d4xPr2bVr2s6t/tvtn6l9/h3hgCtnbOUAi/ikPAAAAACCF78yth48ePDgwYPmr+IE3sIZI3mex4K6+vXr169f3xLclS9fvnz58tZ8kTO5qYR9TktdAaGsnel+rwS4quPyalwYp8ejK9hUlbL+sD0WuMTHx8fHx7t3nfMrdz/55JNPPvnEfBxV50tlh78vLCRnIS+/gpkF5TVq1KhRo4b7mWsBAMEH/y68+eabb775pv/+p0+fPn36dKJdu3bt2rXLf/8guNixY8eOHTvM23Xs2LFjx47u96eoefnll19++WWi+/fv379/X7/dlClTpkyZ4l2/xo8fP378eKJ79+7du3fPOz+BSlZWVlZWVlH3AgAAAAAAeA2ErQAAUMRwxlZ+VZ0obNUNHLkVgBL3i9jth9N+y9qb9s/twKzbx+nUn+44qer9f+zdd1gUV9s/8DtRAUEUpIOgGCwooqKICnZjiSWoEYxiCVFj7MYWE2JQo6R62RIfG5aIxt5iiYhRFFusWAOoiAYiUgQBKcbn94fXfc37Tt75zezubMPv55+5dnfmnLMr4Mye79xH0+fl2pU7Tu1+5PbXdLxy49P0dW3303bc/HMvDrbyRCwAAABUHu7u7u7u7kKQUd8OHz58+PBh/fcDmuGK/Pb29vb29sKS6I0bN27cuDGRi4uLi4uLELjj80YO7PFWfD6p7+spuf4MFVR9XbbaBoaZ0vZ5KWyuJKyW69evX79+nejs2bNnz57V/P1qGoBl/D2OnZ2dnZ2d8PvFwda33nrrrbfeEq67+IZmAIDx48ePHz+eqG/fvn379jVcvxzI4yXR+QYBgP8LV/pVysPDw8PDg8jLy8vLy0t/4zK0M2fOnDlzRriRRqmuXbt27dpVf0HfHTt27Nixg+i333777bff1G/fXKBiKwAAAMDrAcFWAAAj4wkRnlDkoBkH0KQmVKQmlMS0nYDSdKu0XUOPS64fqc9L6fPGouv70vbfRdt2daVre5r+XOj6cyW11TQQoPR9yFUa4sf894UrB3GgHgAAACqfd95555133tF/P7/++uuvv/6q/35ANxyw8/T09PT0FJZEbdiwYcOGDYX9NA36abrV9vxb6fmupsfr2r+m5+1yxysdh777kdpf2+P5+47IyMjIyEihsrBa9u7du3fvXqLHjx8/fvxY9wrA4vHz/hwYd3Z2dnZ2JvLz8/Pz8xMq0nKFZL5hGQBAjL/vjY2NjY2NFb6fMZS7d+/evXuXaPr06dOnTzdcv2BeONCpVEhISEhIiP7GY2glJSUlJSVE48aNGzdunPLvpflGFn1VZi4uLi4uLiaaMWPGjBkz1G/f3PDfMwAAAACo3HCvOACAkfEXmvzFh7W1tbW1tRA4e/78+fPnz7WfgBMHZMVfxIhfFz9WOn6p46XaEy95LjcutT5nbd+npu3rm1Q/Sp+Xeiw3frn25frRdn+p43TdajrBra9xyZEbt3g/cYCA/57wBCwvPYuKrQAAAJUXVwJbsWLFihUr9NfP8ePHjx8/Lky0coASTAsH8vi6k7dcwY0n8LOzs7Ozs4VKbuLKrRxIlAom8n58faR0K3W8FKn9dD3e2KSuDzR9XulxStuV2l/pdQ4/5kqm3bp169atG1F8fHx8fLz0+JUqLy8vLy8n2rp169atW4UgitQNw1LXTVLP8+8LV5zlyqxcGZuDafx7pnZwFwAqHycnJycnJ6L169evX79euCFJ6fdEulqzZs2aNWuI3n777bfffpto8ODBgwcP1n+/YNqysrKysrI0r4QZHBwcHBysv3EZ2tixY8eOHStUhldq5syZM2fOJGrVqlWrVq3UH9eiRYsWLVpElJGRkZGRIb8/n4/w9aCjo6Ojo6P641IL36i0ZcuWLVu2yO9///79+/fvm+55PQAAAACoA8FWAAATw4EzDqDxF0qlpaWlpaX/3l9uIkl8Ya/pYzlSX7hqGvTk/fgLF6XtivdTOsGq1rgNHWgV03QiUmo/pftre7zUfkrHq+nxcs9LTVzK9avpVtt21Oqf3xcvNctLgvGEKwAAAFRenTt37ty5s3B9UVRUVFRUpH4/fJ1y9OjRo0ePEg0YMGDAgAHq9wPq4OsXrihZp06dOnXqCIG9y5cvX758mSglJSUlJUUIvIorhYrbkwqqKsXnr2oFVcXn1VLHS+2n9HipdtQmdZ2g6Xjkrjc07Vfb65R+/fr169eP6Pbt27dv3yZ69OjRo0ePlH8eUv7666+//vqLKCEhISEhQVgKWHx9JH4sV1mYK866u7u7u7sTBQUFBQUFCX9fAQC01atXr169egmB/JUrV65cudJw/Y8fP378+PFCMJH/zsHrKSkpKSkpSfPjKkuw9Ycffvjhhx+I4uLi4uLilB/n6+vr6+tL9OWXX3755ZfqjystLS0tLU0Yn1IjRowYMWIE0ccff/zxxx+rPy61cYEXpcFWvrGSK/YbugI2AAAAABgG7h0HADAxPGHCd9A6ODg4ODgIlY+4Yo64co7SLdN2AkrbdsWUHi/3vFS7mi4VqS19tau0X7nnNf38lfZnqM9TaeCUaboEqqbvS9P3rekSl1L9yI1XbiKW/45wwJUrDgEAAEDlZWlpaWlpKVTi0reff/75559/1n8/oK4qVapUqVJFWDmkSZMmTZo0IQoICAgICBCuQ/n8Unw9qvT8W+l5udLzXqWPpa4vNL2xTdvxq7UVkxunXHu6jl/X4/mG1JEjR44cOVL9G+9Onjx58uRJoZKX1M+J+Hn+uba3t7e3tydq2bJly5Ytibp06dKlSxch0Mp/XwEA1LJ48eLFixcT+fn5+fn5Ga7fnJycnJwcolGjRo0aNcrw32+CadE02Gpra2tra0vUvHnz5s2b629c+hYTExMTEyNUXFWKbxTbsGHDhg0b9Hd+MGXKlClTphCVlZWVlZXJ788rd/H7MhdckEFTmlYYBgAAAADzgmArAICJ4aXBufKHnZ2dnZ2dMNGodOKOKZ0g03SiSkyqPan2pY5Xa6t0HGq9bq5bbf8d5f79lH5emtLX+9a0H7XGI9eOthPTPDHME7JcgYu/2OQAAwAAAFR+ffv27du3r/77+fXXX3/99VeiJ0+ePHnyRP/9gTr4vJCvQ7nSES8Z7+3t7e3tLdx4yfsxuaCr+HxV6fO6ng9rGnhVutV0/IbaKg306vo+1RoPb/nGu/79+/fv31+9n2tuf9euXbt27RIqgEkFlLkiL3//wsEKDpg1bdq0adOmRHXr1q1bty5WwAAA9XFAbtOmTZs2bfr3/7f6Fh8fHx8fT7Rs2bJly5YZrl8wLZoGW9u2bdu2bVvz+56xoqKioqKCaOrUqVOnTiX67LPPPvvsM+XfG/MNOhs3bty4cSNRmzZt2rRpo/449+/fv3//fqJDhw4dOnRI+XFRUVFRUVHmV8GUz7M0hWArAAAAQOWGYCsAgIniL0i4Qg5XclVrokrb45jS/cTtSx0vfl7TfuRo2o/U8drup+14Nf130Pb9SfUv9VjT49XaT9Ottsfr2q9aE9tSn4NcMICD8Q0aNGjQoIEQaAUAAIDXDwdb+fpCX3iCWOnSkWDaOOAXEhISEhJC5O/v7+/vT1SrVq1atWoJP0/iQKtcwFV83ip1vHiFEqVBS12vi+WOZ/q+DtB0fHLjUjo+fQVkxVvxvzMvYcwVg9VSWFhYWFhIdPjw4cOHD0uPh1e04OunZs2aNWvWTHjMFekAAPSNK0XPnz9//vz5hu9/9uzZs2fPJkpOTk5OTjZ8/2AcvKT71atXr169qvw4Pk80F7du3bp16xZR+/bt27dvT7R06dKlS5dq3s7XX3/99ddfE4WFhYWFhak/Tq7MOmPGjBkzZig/zsfHx8fHh2jy5MmTJ09Wf1z6VqdOnTp16mgelEawFQAAAKByQ7AVAMBEccUQDrSKA648kajrBBlTaz+p45iuE4X63sr1L6bp61ITaUonUrV9H3LvS9yvrv8Ocp+P1Oel7ecq157S45W2q+3nL9WOXLtKfz74df474e7u7u7uLvz9AAAAgNePs7Ozs7OzsIS2vvFSnGDeeEKZVw7hCpYBAQEBAQFEgYGBgYGBQmVXvn6VOn+Vu+6RC6oqPY7JtSt3nq30eW3303Sra/9y71/b6xBNj5fbPzw8PDw8XP0g6fXr169fv0508+bNmzdvCj/fjRo1atSoEdHbb7/99ttvE7Vo0aJFixbCdRRXTDS3SnQAYP54SfSuXbt27drVcP1yoG7o0KFDhw4VKl5D5XbhwoULFy4IN6opxQFRU5WdnZ2dnS1UZOXz2IsXL168eFHz9jhoyr+f+vLNN9988803RKmpqampqcqPW7JkyZIlS4gsLS0tLS31Nz594Yr4bm5ubm5uyo9DsBUAAACgckOwFQDARPHEIE+k8IQiV17kC325iSFtt2Jqt2/o8ej6PqSO13Rcxv5cpfqXG4++Pj9tPydtP3e13o+u71vbnwO5iWH+4pIngnnJWF7SDgAAAF5fERERERER+u+HKz1pWvEJTBufV/KS7BwA5GCgg4ODg4ODcIMVX8/y+aq4QqdagVBNz891PV5p+2q3q23/cp+zrsfpur/4ef7egyug8c+RWn777bfffvtNCKpyZVauOMcVWmvXrl27dm31+gUA0BQXNNi0adOmTZsM/3eJbwTgQCBUbmfOnDlz5ozy/bnSedu2bdu2bau/cWkqPT09PT2daNKkSZMmTSKqV69evXr1iGJiYmJiYoTgtlJ8vsCVXb/77rvvvvtOX6MXxs8VYZV655133nnnHaI+ffr06dNHb8MzmLp169atW1f5/vfv379//77+xgMAAAAAxoVgKwCAmeBgmpOTk5OTk/BYaiJJ2wk1JjfhpO1W3L7cfpqS60/p8Zo+r/b70Jamn7dcO2r1o+vPi67vQ9f3r/b70nQrNUHMwQCe8PX29vb29ha2HHTV99LDAAAAYPref//9999/33A3vKxbt27dunX67wcMi887+eeIzzt79erVq1cvIehao0aNGjVqCOetL168ePHixb8DrnKBV123UufTcs9ru5/c8Zq2o+v1vVw7Sj8/3jKln7+m+/OWA6Zt2rRp06aNej+/paWlpaWlRIcOHTp06JCwZC8AgKny8PDw8PAgWr169erVqw3fPwf6+O8mVE6nT58+ffq08v35Bic+3zM0Dl5zZVO+QYVXElixYsWKFSu0rzjMK1/t3r179+7dRJMnT548ebL670Ns2rRp06ZNUz5uLoiyePHixYsX6398huLp6enp6al8f1RsBQAAAKjcqhp7AAAAoAxXaK1Vq1atWrWIiouLi4uLicrLy8vLy4UJGp4I4iCb1ISW+HXx0pFi4uN0l8V4RwAAIABJREFUJdef2u0q7U/X4zVtV4qm/ajVrvh1TduVO15uP6XPy/UvtdV0f7l21GpPvJWbUObnuXIAV8bipZq4ohb/vqpd6QgAAADMj729vb29PVH//v379+9PtH379u3bt+uvv9jY2NjYWKLo6Ojo6GihoieYNz6v5PNQnvjnLU/Ec/C1oKCgoKCAKCcnJycnhyg3Nzc3N/ff57vi6yV+LL7+5OeVbsXtyRGf74uPk7oekNpPX9eBcvtJXf/IPZa77lG6v67XQfy4d+/evXv3Fipx8ZLCuuIliFetWrVq1SqiTz/99NNPP9W9XQAAfRk0aNCgQYOIRowYMWLECKGSq77x3+PIyMjIyEii5OTk5ORkImdnZ2dnZ/33D/rF/++eO3fu3Llzyo/jipqXLl26dOmS8uN4HoPnNQoLCwsLC4V5jWfPnj179ozo4cOHDx8+JEpLS0tLSxO2qampqampwnFqCw4ODg4OJlq7du3atWuJGjdu3LhxY/X7ETty5MiRI0eI9u7du3fvXuXHceCWbyyrLLjSrlKZmZmZmZnCzxFWLgMAAACoXBBxAACz8eqLtAULXj2KijLuaIyPJ3R4++TJkydPnghfSPGSQDwRqHSrdIJQfBwTvy4+TryfWs9rup/c8XL7ydF0fzmaTlwq3U/qOLmJSTFxRR6lx+s6Eaq0gpFcQFTp6+L9+LHckqri16XaF1ey4v2kKlxxoJWDrK1bt27dujWRi4uLi4uL/M8DAAAAvH644pahlqr86quvvvrqK6LPP//8888/139/YBr4/JWDC1xZ6/r169evXxee5/34vFfuOpUpvW6V2l/8vJjS6zm1rh/FtL2+0/R5Ta/TxMTXN3LHK72+Ej/mwAIHTfh6SFf8vUlSUlJSUpL6FWIBANRWVFRUVFREFBAQEBAQIAT9DCU0NDQ0NJRoz549e/bsMVy/oB8cVG7evHnz5s2NPRrDs7a2tra2Jpo7d+7cuXOJZsyYMWPGDOEGLn3joK+/v7+/vz/Rn3/++eeff8ofx9/78v5cCKWy+Omnn3766SeiCRMmTJgwQflxt2/fvn37tuECyQAAAABgGFiUFgDATNna2tra2hLZ2dnZ2dkJX7jIBemY0uCf3FYuEKi0HalxKX1e0/3kjpfbT47c+1TrOE3b1XQ/tfpXSum/v9JxaduO1H5yx4ufFwd+xfuJg7FKx8tbDrQ2bNiwYcOGxlsCDAAAAMxHz549e/bsSVSnTp06derov79ly5YtW7ZM+6VAwTxxIJUDA7y0fIcOHTp06CAsFVuzZs2aNWv++7xYbisVkJTbT+6GNPF5utx1ra7Ha9uf3A1zcsdpex0v9znKbZV+buJ/RycnJycnJ6LOnTt37txZvZ9TDlYPGzZs2LBhQmAMAMBU8fc+GzZs2LBhg+ECeIwrSvKNBmDezpw5c+bMGWOPwnAsLCwsLCyIxowZM2bMGCEIOXv27NmzZxv+92nx4sWLFy9WHmhlMTExMTExlS/QyrgisKbu3bt379499ccDAAAAAMZlwFN0AADdvFrCsmvXV486djTuaIyPv2jhSjB8hy9P/FRUVFRUVGhewUbqsZimFWzEgT216FpxR98Ve/h9a1qxR9PPS+n+UvuJnxdPMOqrP037kTtO6f6a7ic14arphLX4eLnH4i3/HPFSr/xFX/369evXr09kaWlpaWn570rKAAAAAIzPEx4/fvz48WOhUqG+cGVOPm9p1apVq1at9NcfmAY+b+XrVj5/5SArv16tWrVq1aoJKxHwlo/j61q5G8HkHstdvyg9Tu66Renrmo5Lrl21jpd733Ljl7v+URqsFf988M8PV5RLT09PT08XVq7RVV5eXl5enrDt27dv3759dW8XAEBfPD09PT09hYB+YmJiYmKi4fo/fvz48ePHiQYNGjRo0CDhxmswL0uXLl26dKlQubWycXV1dXV1JZo4ceLEiROJfv75559//pkoIiIiIiLCeMHQR48ePXr0iCg8PDw8PFyY15ETGBgYGBhItGLFihUrVqi/Ypyp4M9j5cqVK1euVH5cu3bt2rVrhwr8AAAAAJVNJTzlBYDK6tVEx4IFrx5FRRl3NMYnnvjhCb8HDx48ePCAKCMjIyMjQ5gQ5Als8WPx0o7i55nU/lJb8fFy+ysN2sq1K3e8mNLjpaj1BRK3IzcxKaZ0f7UmMnU9XtMJUqVbpRWLNH3MW10rEokrDon7k6tExRMVVlZWVlZWRN7e3t7e3sLWw8PDw8ND+ucZAAAAQCwlJSUlJYXI19fX19dXutK8Who1atSoUSOiW7du3bp1CzfivK74PJjPb8XnvbzkPF/XciUtDkiLg4/i61wxqZ8zba9H1bpOVHr9p+n1oRTx9YlcP1LXXVKvyx2nNNDKPw8ccOYVatzc3Nzc3IQgF7/OFYA5kKqWffv27du3j6h///79+/dXr10AALXx/6f89/DcuXPnzp0zXP98w9LZs2fPnj0r3JAA5oFvlL9///79+/eNPRrteXl5eXl5EfXu3bt3795E77777rvvvkvUvXv37t27m97P5ZAhQ4YMGUK0bdu2bdu2ye/P5418QyIHOCurwsLCwsJCzYPH06ZNmzZtmlAJFwAAAAAqh6rGHgAAAGhHPJHHS+nwklRcCYeX/BRPAIrbYXITVOJ2pAKnvL+2gU258YnbFT8vPl7cv1rjUmuikenantKJSqnXpf7dlbav64Sn3FauXaXvT+lWauJV7f3lJnirVq1atWpV4fealw62t7e3t7dHMAQAAAA017Bhw4YNGxL169evX79+QpBLX3iJzZ07d+7cuZMoLCwsLCxMf/2BaeLrKA4YiIMGLi4uLi4uwkoEtWvXrl27NlF2dnZ2draw5SBjaWlpaWmp9Iol4usFqUCrVBBVafBV/LzcdYrcda74eSlKr4fE1xtS19NKr8PEj7W97hF/j8HBFAcHBwcHByJbW1tbW1thy9dDHHhdvXr16tWrid5777333ntP/nNQ6sMPP/zwww+FCnYcrAUAMDX8fVFcXFxcXBxRixYtWrRoQfTs2bNnz57pv/9Lly5dunSJaP78+fPnzydasGDBAi5LAaaLbyQytUCr+HyAV3wQb318fHx8fIjatm3btm1b4XtSU8eVjpUGWhlXmK3sgVbG53v8vXd+fn5+fr78cffu3bt3757+xwcAAAAAhoVaXgBgNl5NfKBiqxy+0M/JycnJyRG2POHHlFZwlQqwavo8k5tIlJow1HbiUdMJSqn9lD6vKal2lE5QSpE6XunzUhOZUscpPV7TCVNx5TCpCVK555VWVtV1P3HFKfH+UpVfpSq18vF8hzpXZuUlOHlJTgAAAABtceWfkJCQkJAQ/ffHlaG4EicH2wD+f8SVXHkJV77+5etdvr7i82leylR8vaHp9ajcY6XXh2pdR2p7vSd33aXpdaHcjX2Mf885yMxBLA6wcJCVr3N46WA+Tu5zGzFixIgRI4QlhtXSo0ePHj16EB05cuTIkSNYGQMATF9sbGxsbKwQ0DcU/v43ISEhISGBqHPnzp07dzZc/6AZPm/i8ytD4f/X+ftMrsDOK1RVdjxPwxVJleLzImtra2tra/2Nz9Q8fPjw4cOHwg1scvjnyN3d3d3dXf/jAwAAAADDwFdxAGA2Xk2MINgqh5egKikpKSkpESb8nj59+vTpU6GCq1SgVRxQVRpkFT9mckFZ8X5MbqJR2wlGucdqP29o2k5wih9L7S+3n9LnNZ1YFe8nN4EqFSwVP9Z1K25PKrgqfp2Pk9qff554wtfPz8/Pz4/I29vb29tbmACWWnIVAAAAQFPBwcHBwcFEZ86cOXPmjP77W7FixYoVK4gmTJgwYcIE/fcH5q2srKysrOzfW67c+vjx48ePHwvn1wUFBQUFBUTp6enp6elCgIPPt+WuUzW9jtQ12MrPy12Hiel6nSe+npEidf0ldV3E74evV7hCdL169erVq0fk7Ozs7OwsBBA48MpBF3GgVe7zLSoqKioqIgoICAgICCBKTU1NTU1V/jnKWbZs2bJly4gmTZo0adIk9doFANCX8PDw8PBwou3bt2/fvt1w/Xp6enp6ehJdu3bt2rVrQsVFAAAAAAAAAG2YQAQHAECZVxMlCLYqxXey8lKNubm5ubm5wsQfTzyJg6lyQVfxVumEoNL9maYTjJo+L/VY7ecNTWkgVdvHcvvJPa/pfnIBVk2P0zS4Kg6iKt1f0/bFz3NwlZdi5Ylg3HEOAAAA+rJnz549e/YQDRw4cODAgfrvz8nJycnJiSgtLS0tLU1YchJAE8XFxcXFxcKNnHw+zc9z4JVv/OQKrrwfB2B5P/F1nfi6Re76VIrS60i56zml+2l7fSbVrjgQzAFUDqbyVlx5jbe88gRXHLOzs7OzsxNu5FMLB/M7duzYsWNH4XpLV5aWlpaWlkQXLly4cOECkb+/v7+/v+7tAgDoC1c050rYXPnQUHjpdLUraQMAAAAAAMDrBTW+AMBsREdHR0dHd+366lHHjsYdjekTB0l5IoortkpViNS0faXPy+2n6wQePy/XrtzEnrbUakff/cp9Htrup+mEqdr7yR2nNCDLNA3AituXel7qdd4yR0dHR0dHoiZNmjRp0kSocMGVjAAAAADU1qhRo0aNGhHt2LFjx44dwlKZ+sJBQ67M2KVLly5duuivP6ic+OeHg9G1atWqVauWcD7NFUI5WOnm5ubm5iZs+frxyZMnT548EYKWcisjiK87pa4H1L5ekdtP7vqDH/P4+TEHQOWu5zmoyhVX+XOtX79+/fr1hb8jfB3j6+vr6+sr3LDHS+iKV2xRC1cK5JVsEhMTExMTdW+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    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div>\n",
    "<center>    \n",
    "<img src=\"attachment:db60916d-155e-4465-b859-e6a66f49b865.png\" width=\"300\"/>\n",
    "</center>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find water-water hydrogen bonds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Basic usage of HydrogenBondAnalysis involvees passing an acceptor atom selection (`acceptors_sel`) and a hydrogen atom selection (`hydrogens_sel`) to `HydrogenBondAnalysis`. By not providing a donor atom selection (`donor_sel`) we will use the topology bond information to find donor-hydrogen pairs.\n",
    "\n",
    "In the following cell, `acceptors_sel=\"name OH2\"` and `hydrogens_sel=\"name H1 H2\"` will select the oxygen and hydrogen atoms, respectively, of water. The names correspond to those for the CHARMM TIP3P water model and may be different for other force fields.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "hbonds = HydrogenBondAnalysis(\n",
    "    universe=u,\n",
    "    donors_sel=None,\n",
    "    hydrogens_sel=\"name H1 H2\",\n",
    "    acceptors_sel=\"name OH2\",\n",
    "    d_a_cutoff=3.0,\n",
    "    d_h_a_angle_cutoff=150,\n",
    "    update_selections=False\n",
    ")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "    \n",
    "**Note**\n",
    "    \n",
    "For a performance boost, `update_selections` can be set to `False`.\n",
    "    \n",
    "However, always set `update_selections` to `True` if you think that your selection will update over time. For example, the number of oxygen atoms within 3.0 <span>&#8491;</span> may change over time if you choose `acceptors_sel=\"name OH2 and around 3.0 protein`.\n",
    "    \n",
    "See also the MDAnalysis [documentation on updating AtomGroups](https://docs.mdanalysis.org/stable/documentation_pages/selections.html#dynamic-selections).\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then use the `run()` method to perform the analysis. If we do not set the `start`, `stop`, and `step` for frames to analyse, all frames will be used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "538bc5e20f844f0fb97f44c35a2da468",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/10 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<MDAnalysis.analysis.hydrogenbonds.hbond_analysis.HydrogenBondAnalysis at 0x14115fdf0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hbonds.run(\n",
    "    start=None,\n",
    "    stop=None,\n",
    "    step=None,\n",
    "    verbose=True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Accessing the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are stored as a numpy array in the `hbonds.results.hbonds` attribute. The array is of shape $(N_\\textrm{hbonds}, 6)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(27, 6)\n"
     ]
    }
   ],
   "source": [
    "# We see there are 27 hydrogen bonds in total\n",
    "print(hbonds.results.hbonds.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each row of the results array contains the follwing information on a single hydrogen bond:\n",
    "\n",
    "`[frame, donor_index, hydrogen_index, acceptor_index, DA_distance, DHA_angle]`\n",
    "\n",
    "Let's take a look at the first hydrogen bond found:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  0.           9.          10.           3.           2.82744082 150.48955173]\n"
     ]
    }
   ],
   "source": [
    "print(hbonds.results.hbonds[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This hydrogen bond was found at frame 0. The donor, hydrogen, and acceptor atoms have indices 9, 10, and 3, respectively. There is a distance of 2.83 <span>&#8491;</span> between the donor and acceptor atoms, and an angle of 150<span>&#176;</span> made by the donor-hydrogen-acceptor atoms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The frame number and atom indices can be used to select the atoms involved in the above hydrogen bond. However, as the results array is of type `float64`, these values must first be cast to integers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hbonds.results.hbonds.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "first_hbond = hbonds.results.hbonds[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "frame, donor_ix, hydrogen_ix, acceptor_ix = first_hbond[:4].astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# select the correct frame and the atoms involved in the hydrogen bond\n",
    "u.trajectory[frame]\n",
    "atoms = u.atoms[[donor_ix, hydrogen_ix, acceptor_ix]]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AtomGroup with 3 atoms>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "atoms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For clarity, below we define constants that will be used throughout the rest of the notebook to access the relevant column of each hbond row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "FRAME = 0\n",
    "DONOR = 1\n",
    "HYDROGEN = 2\n",
    "ACCEPTOR = 3\n",
    "DISTANCE = 4\n",
    "ANGLE = 5\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Helper functions\n",
    "The are three helper functions that can be used to quickly post-process the results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. Count by time.** Counts the total number of hydrogen bonds at each frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(hbonds.times, hbonds.count_by_time(), lw=2)\n",
    "\n",
    "plt.title(\"Number of hydrogon bonds over time\", weight=\"bold\")\n",
    "plt.xlabel(\"Time (ps)\")\n",
    "plt.ylabel(r\"$N_{HB}$\")\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. Count by type.** Counts the total number of each type of hydrogen bond.<br>\n",
    "\n",
    "A type is a unique combination of donor residue name, donor atom type, acceptor residue name, and acceptor atom type.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([['TIP3:OT', 'TIP3:OT', '27']], dtype='<U21')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hbonds.count_by_type()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Each row contains a unique hydrogen bond type.<br>\n",
    "The three columns correspond to:<br>\n",
    "\n",
    "   1. the donor resname and atom name (here, the OT atom of the TIP3 water residue)\n",
    "   2. the acceptor resname and atom name (here, the OT atom of the TIP3 water residue)\n",
    "   3. the total count\n",
    "   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The average number of each type of hydrogen bond formed at each frame is likely more informative than the total number over the trajectory. This can be calculated for each hydrogen bond type as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TIP3:OT to TIP3:OT: 1.08\n"
     ]
    }
   ],
   "source": [
    "for donor, acceptor, count in hbonds.count_by_type():\n",
    "    \n",
    "    donor_resname, donor_type = donor.split(\":\")\n",
    "    n_donors = u.select_atoms(f\"resname {donor_resname} and type {donor_type}\").n_atoms\n",
    "    \n",
    "    # average number of hbonds per donor molecule per frame\n",
    "    mean_count = 2 * int(count) / (hbonds.n_frames * n_donors)  # multiply by two as each hydrogen bond involves two water molecules\n",
    "    print(f\"{donor} to {acceptor}: {mean_count:.2f}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "    \n",
    "**Note**\n",
    "\n",
    "In a water-only system the average number of hydrogen bonds per water molecule should be around 3.3, depending on temperature and forcefield. We don't see this due to the small system size (15 water molecules).\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3. Count by ids.** Counts the total number of each hydrogen bond formed between specific atoms.<br>\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12, 14,  9, 10],\n",
       "       [ 9, 10,  3,  9],\n",
       "       [ 3,  5,  0,  4],\n",
       "       [ 0,  1,  6,  3],\n",
       "       [ 6,  7, 12,  1]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hbonds.count_by_ids()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each row contains a unique hydrogen bond.<br>\n",
    "The four columns correspond to:<br>\n",
    "\n",
    "   1. the donor atom index\n",
    "   2. the hydrogen atom index\n",
    "   2. the acceptor atom index\n",
    "   3. the total count\n",
    "   \n",
    "The array is sorted in descending total count. You can check which atoms are involved in the most frequently observed hydrogen bond:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Most common donor: <Atom 13: OH2 of type OT of resname TIP3, resid 21 and segid WAT>\n",
      "Most common hydrogen: <Atom 15: H2 of type HT of resname TIP3, resid 21 and segid WAT>\n",
      "Most common acceptor: <Atom 10: OH2 of type OT of resname TIP3, resid 15 and segid WAT>\n"
     ]
    }
   ],
   "source": [
    "counts = hbonds.count_by_ids()\n",
    "most_common = counts[0]\n",
    "\n",
    "print(f\"Most common donor: {u.atoms[most_common[0]]}\")\n",
    "print(f\"Most common hydrogen: {u.atoms[most_common[1]]}\")\n",
    "print(f\"Most common acceptor: {u.atoms[most_common[2]]}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further analysis\n",
    "\n",
    "There are many different analyses you may want to perform after finding hydrogen bonds. Below we will calculate the mean number of hydrogen bonds as a function of $z$ position of the donor atom.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# bins in z for the histogram\n",
    "bin_edges = np.linspace(-25, 25, 51)\n",
    "bin_centers = bin_edges[:-1] + 0.5\n",
    "\n",
    "# results array (this is faster and more memory efficient than appending to a list)\n",
    "counts = np.full(bin_centers.size, fill_value=0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "for frame, donor_ix, *_ in hbonds.results.hbonds:\n",
    "\n",
    "    u.trajectory[frame.astype(int)]\n",
    "    donor = u.atoms[donor_ix.astype(int)]\n",
    "    \n",
    "    zpos = donor.position[2]\n",
    "    hist, *_ = np.histogram(zpos, bins=bin_edges)\n",
    "    counts += hist * 2  # multiply by two as each hydrogen bond involves two water molecules\n",
    "\n",
    "counts /= hbonds.n_frames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(bin_centers, counts, lw=2)\n",
    "\n",
    "plt.title(r\"Number of hydrogen bonds as a funcion of height in $z$\", weight=\"bold\")\n",
    "plt.xlabel(r\"$z\\ \\rm (\\AA)$\")\n",
    "plt.ylabel(r\"$N_{HB}$\")\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may wish to find the number of hydrogen bonds in $z$ per unit area in $xy$, rather than the total number a each $z$ position. To do this, simply divide `counts` by the mean area in $xy$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean_xy_area = np.mean(\n",
    "    [np.prod(ts.dimensions[:2]) for ts in u.trajectory[hbonds.frames]]\n",
    ")\n",
    "counts /= mean_xy_area\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "    \n",
    "**Note**\n",
    "    \n",
    "It is likely you will want to calculate the distance from an interface, such as a lipid membrane, rather than the absolute position in $z$. For example, if you have a bilayer that is centered at 0, you might define your interface as the mean position in $z$ of the phosphorous atoms in the upper leaflet of the bilayer:\n",
    "    \n",
    "    headgroup_atoms = u.select_atoms(\"name P\")\n",
    "    interface_zpos = np.mean(headgroup_atoms.positions[:, 2])\n",
    "    \n",
    "    zpos = donors.positions[:,2] - interface_zpos\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Store data\n",
    "There are various ways of storing the results from the analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. You can persist the HydrogenBondsAnalysis object using pickle (or joblib)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"hbonds.pkl\", 'wb') as f:\n",
    "    pickle.dump(hbonds, f)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"hbonds.pkl\", 'rb') as f:\n",
    "    hbonds = pickle.load(f)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. You can extract the results and store the numpy array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.save(\"hbonds.npy\", hbonds.results.hbonds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. You can create a Pandas DataFrame with more information about hydrogen bonding atoms, which may make some further analysis easier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(hbonds.results.hbonds[:, :DISTANCE].astype(int),\n",
    "                  columns=[\"Frame\",\n",
    "                           \"Donor_ix\",\n",
    "                           \"Hydrogen_ix\",\n",
    "                           \"Acceptor_ix\",])\n",
    "\n",
    "df[\"Distances\"] = hbonds.results.hbonds[:, DISTANCE]\n",
    "df[\"Angles\"] = hbonds.results.hbonds[:, ANGLE]\n",
    "\n",
    "df[\"Donor resname\"] = u.atoms[df.Donor_ix].resnames\n",
    "df[\"Acceptor resname\"] = u.atoms[df.Acceptor_ix].resnames\n",
    "df[\"Donor resid\"] = u.atoms[df.Donor_ix].resids\n",
    "df[\"Acceptor resid\"] = u.atoms[df.Acceptor_ix].resids\n",
    "df[\"Donor name\"] = u.atoms[df.Donor_ix].names\n",
    "df[\"Acceptor name\"] = u.atoms[df.Acceptor_ix].names\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.to_csv(\"hbonds.csv\", index=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] Richard&nbsp;J. Gowers, Max Linke, Jonathan Barnoud, Tyler J.&nbsp;E. Reddy, Manuel&nbsp;N. Melo, Sean&nbsp;L. Seyler, Jan Domański, David&nbsp;L. Dotson, Sébastien Buchoux, Ian&nbsp;M. Kenney, and Oliver Beckstein.\n",
    "<span class=\"bibtex-protected\">MDAnalysis</span>: <span class=\"bibtex-protected\">A</span> <span class=\"bibtex-protected\">Python</span> <span class=\"bibtex-protected\">Package</span> for the <span class=\"bibtex-protected\">Rapid</span> <span class=\"bibtex-protected\">Analysis</span> of <span class=\"bibtex-protected\">Molecular</span> <span class=\"bibtex-protected\">Dynamics</span> <span class=\"bibtex-protected\">Simulations</span>.\n",
    "<em>Proceedings of the 15th Python in Science Conference</em>, pages 98–105, 2016.\n",
    "00152.\n",
    "URL: <a href=\"https://conference.scipy.org/proceedings/scipy2016/oliver_beckstein.html\">https://conference.scipy.org/proceedings/scipy2016/oliver_beckstein.html</a>, <a href=\"https://doi.org/10.25080/Majora-629e541a-00e\">doi:10.25080/Majora-629e541a-00e</a>.\n",
    "\n",
    "[2] Naveen Michaud-Agrawal, Elizabeth&nbsp;J. Denning, Thomas&nbsp;B. Woolf, and Oliver Beckstein.\n",
    "<span class=\"bibtex-protected\">MDAnalysis</span>: <span class=\"bibtex-protected\">A</span> toolkit for the analysis of molecular dynamics simulations.\n",
    "<em>Journal of Computational Chemistry</em>, 32(10):2319–2327, July 2011.\n",
    "00778.\n",
    "URL: <a href=\"http://doi.wiley.com/10.1002/jcc.21787\">http://doi.wiley.com/10.1002/jcc.21787</a>, <a href=\"https://doi.org/10.1002/jcc.21787\">doi:10.1002/jcc.21787</a>.\n",
    "\n",
    "[3] Paul Smith, Robert&nbsp;M. Ziolek, Elena Gazzarrini, Dylan&nbsp;M. Owen, and Christian&nbsp;D. Lorenz.\n",
    "On the interaction of hyaluronic acid with synovial fluid lipid membranes.\n",
    "<em>Phys. Chem. Chem. Phys.</em>, 21(19):9845-9857, 2018.\n",
    "URL: <a href=\"http://dx.doi.org/10.1039/C9CP01532A\">http://dx.doi.org/10.1039/C9CP01532A\n",
    "\n"
   ]
  }
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